Dielectronic recombination. I. General theory

In the process of dielectronic recombination (DR), radiative capture of an electron by a positive ion occurs via compound resonance states of the electron+ion system (states with two or more electrons excited). These states can decay by autoionisation, with probability A, or by radiative stabilisation, with probability R. In general, these are competing processes: one may have A>R or A<R. It is assumed that wavefunctions have been obtained for the electron+ion system, allowing for resonances but neglecting interactions with the radiation field. The interactions are then handled using the general formulation of the problem given by Davies and Seaton (1969). A scattering matrix S is calculated allowing for radiative channels. It has submatrices S ee , which describes electron-electron scattering allowing for radiative decays, and S pe , which describes photon emission following electron capture. Using the unitarity of S, the total DR rate can be expressed in terms of S ee .